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This paper introduces two new techniques for speech compression using wavelet transforms (WT). The first technique, zero wavelet transform (ZWT), eliminates the high frequency coefficients of the wavelet decomposition with energy values below a certain threshold level. The second technique, average zero wavelet transform (AZWT), in addition to fulfilling the goal of the first technique, averages the approximate coefficients of the wavelet decomposition. These coefficients are almost constant at higher decomposition levels of the transform. The wavelet coefficients are then quantized using Lloyd's algorithm and coded using the entropy coding technique before being transmitted. At the receiver end, the received signal is decoded and dequantized before being processed.